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Pythagorean theoremGeometryMiddle schoolabout 1:36

A right triangle has hypotenuse 10 and one leg 7. Find the other leg: animated lesson

A narrated, step-by-step pythagorean theorem video lesson with captions. Final answer: b = √51 ≈ 7.141428429; area = 24.9949995; perimeter ≈ 24.14142843; angles ≈ 44.427004°, 45.572996°, 90°.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.6 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    A right triangle has hypotenuse 10 and one leg 7. Find the other leg.
  2. 2. Steps, part 1
    1. a2+b2=c2  ⇒  b2=c2−a2a^2 + b^2 = c^2 \;\Rightarrow\; b^2 = c^2 - a^2
      Rearrange the Pythagorean theorem for a leg
    2. b2=102−72=100−49=51b^2 = 10^2 - 7^2 = 100 - 49 = 51
      Substitute and simplify
    3. b=51=51≈7.141428429b = \sqrt{51} = \sqrt{51} \approx 7.141428429
      Take the positive square root
    4. Area=12ab≈24.9949995,P=a+b+c≈24.14142843\text{Area} = \tfrac12ab \approx 24.9949995,\qquad P = a + b + c \approx 24.14142843
      Area and perimeter
  3. 3. Steps, part 2
    1. ∠A=arctan⁡ab≈44.427004∘,∠B=90∘−∠A≈45.572996∘\angle A = \arctan\frac{a}{b} \approx 44.427004^\circ,\qquad \angle B = 90^\circ - \angle A \approx 45.572996^\circ
      Acute angles
  4. 4. The answer
    b=51≈7.141428429b = \sqrt{51} \approx 7.141428429

    b = √51 ≈ 7.141428429

  5. 5. Check
    • Check: a² + b² = 100 and c² = 100, which agree.
    • Angle sum: 90° + 44.427004° + 45.572996° = 180°.

Transcript

The problem. Here is the problem: A right triangle has hypotenuse 10 and one leg 7. Find the other leg. Find the missing leg of a right triangle from the other leg and the hypotenuse.

Steps, part 1. Rearrange the Pythagorean theorem for a leg. Substitute and simplify. Take the positive square root. Area and perimeter.

Steps, part 2. Acute angles. Angle A is opposite leg a and angle B is opposite leg b; the right angle C is 90°.

The answer. So the answer is b equals the square root of 51 approximately 7.141428429; area equals 24.9949995; perimeter approximately 24.14142843; angles approximately 44.427004°, 45.572996°, 90°. In every right triangle the square on the hypotenuse equals the sum of the squares on the two legs. Knowing any two sides fixes the third, and the angles follow from the tangent ratio.

Check. Check: a squared plus b squared equals 100 and c squared equals 100, which agree. Angle sum: 90° plus 44.427004° plus 45.572996° equals 180°.

About pythagorean theorem

Find a missing side of a right triangle with a² + b² = c².

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